Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22590268 | C2 | semidirect |
| 3. #22589596 | C2 | semidirect |
| 4. #22586358 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586282 | C2 | semidirect |
| 7. C71×#3262 | C2 | semidirect |
| 167. #3262 | D71 | semidirect |
| 174. C71 | #12166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590268 | 2 |
| #22590251 | 2 |
| #22589596 | 2 |
| #22586358 | 2 |
| #22586355 | 2 |
| #22586282 | 2 |
| C71×#3262 | 2 |
| #12166 | 71 |